[CvGmt News] Seminari Calcolo delle Variazioni

[alberti at mail.dm.unipi.it]

   Seminari di calcolo delle variazioni

   when: Wednesday, February 16, at 6 pm

   where: Departiment of Mathematics, Sala delle Riunioni

   speaker: Antonio Siconolfi (Roma I)

   title: Aubry set and applications

   abstract: For a given Hamiltonian H(x,p) continuous and quasiconvex in
   the second argument, defined in RN *RN or on the cotangent bundle of a
   compact  boundaryless  manifold, we consider the equation H = c with c
   critical   value,    i.e.   for  which  the  equation  admits  locally
   Lipschitz-continuous  a.e.  subsolutions, but not strict subsolutions.
   We  show  that  there  is a subset of the state variable space, called
   Aubry  set  and denoted by  \A, where the obstruction to the existence
   of such subsolution is concentrated. We give a metric characterization
   of  \A,  and  we  discuss  its  main properties. They are applied to a
   projection  problem  in a Banach space, to the study of the large-time
   behavior of subsolutions to a time-dependent Hamilton-Jacobi equation,
   and  to  construct a Lyapunov function for a perturbed dynamics, under
   suitable stability assumptions.

Reference: http://www.dm.unipi.it/~alberti/files/altrepagine/SeminarioCVGMT/home.html#future

You find this news in the cvgmt preprint server: http://cvgmt.sns.it/news/20050216/

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